Communications in Analysis and Geometry

Volume 25 (2017)

Number 1

A sphere theorem for three dimensional manifolds with integral pinched curvature

Pages: 97 – 124

DOI: https://dx.doi.org/10.4310/CAG.2017.v25.n1.a3

Authors

Vincent Bour (Laboratoire de Mathématiques Jean Leray, Université de Nantes, France)

Gilles Carron (Laboratoire de Mathématiques Jean Leray, Université de Nantes, France)

Abstract

In “Optimal integral pinching results” [Annales Scientifiques de l’E.N.S. 48 (2015), 41–75], we proved a number of optimal rigidity results for Riemannian manifolds of dimension greater than four whose curvature satisfies an integral pinching. In this article, we use the same integral Bochner technique to extend the results in dimension three. Then, by using the classification of closed three-manifolds with non-negative scalar curvature and a few topological considerations, we deduce optimal sphere theorems for three-dimensional manifolds with integral pinched curvature.

Full Text (PDF format)

Received 27 September 2014

Published 9 June 2017